Subgroups — #45686151

Order 33300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659271	C₂	1	1	yes	maximal, characteristic
2	#26012816	C₃	1	1	yes	maximal, characteristic
3	C₅²⋊#66526	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃	1	1	yes	characteristic
5	#16814877	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅²×C₃₇⋊C₃	C₃×C₄	1	1	yes	characteristic
7	#10625191⋊C₃	—	15	2	no	—
8	C₅⋊D₁₈₅	C₂×C₉	1	1	yes	characteristic
9	AGL(1,𝔽₃₇)	—	25	1	no	maximal, Hall
10	C₅⋊(D₃₇⋊C₃)	—	15	2	no	—
11	C₅²×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	#1043⋊C₉	—	37	1	no	maximal, Hall
13	#10625191	—	15	2	no	—
14	#66526⋊C₂	—	25	1	no	—
15	C₅×C₃₇⋊C₃	—	3	2	no	—
16	(C₅⋊D₅)⋊C₉	—	37	1	no	—
17	#3866⋊C₃	—	25	1	no	—
18	D₁₈₅	—	15	2	no	—
19	#66526	—	25	1	no	Hall
20	C₃×#1043	—	37	1	no	—
21	C₅²⋊C₉	—	37	1	no	Hall
22	D₃₇⋊C₃	—	25	1	no	—
23	C₅×C₃₇	—	3	2	no	—
24	C₃×C₅⋊D₅	—	37	1	no	—
25	#3866	—	25	1	no	Hall
26	C₃₇⋊C₃	#1043⋊C₃	1	1	yes	characteristic
27	#1043	—	37	1	no	Hall
28	C₃×C₅²	—	37	1	no	—
29	D₃₇	—	25	1	no	—
30	C₃×AGL(1,𝔽₅)	—	555	2	no	—
31	C₅⋊D₅	—	37	1	no	—
32	C₃₇	#1043⋊C₉	1	1	yes	characteristic, complemented, Sylow
33	C₄×C₉	—	925	1	no	Hall
34	C₃×D₅	—	555	2	no	—
35	C₅²	AGL(1,𝔽₃₇)	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	555	2	no	—
37	C₂×C₉	—	925	1	no	—
38	C₃×C₅	—	111	2	no	—
39	C₃×C₄	—	925	1	no	—
40	D₅	—	555	2	no	—
41	C₉	—	925	1	no	Sylow
42	C₂×C₃	—	925	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	925	1	no	Sylow
45	C₃	—	37	1	no	—
46	C₂	—	925	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₇	C₄×C₉
prime radical, cosocle	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅²⋊#66526	C₄	semidirect
5. #16814877	C₉	semidirect
11. C₅²×C₃₇	C₄×C₉	semidirect
32. C₃₇	#1043⋊C₉	semidirect
35. C₅²	AGL(1,𝔽₃₇)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#30659271	2
#26012816	3
AGL(1,𝔽₃₇)	25
#1043⋊C₉	37